Question 139631
The revenue R (in millions of dollars) of a large retail store can be modeled by R=1.23t^2-2.22t+8.5, where t is the number of years since 1990. Estimate the year in which the store's revenue will reach 90 million dollars? 
:
Replace R with 90 and solve for t
1.23t^2 - 2.22t + 8.5 = 90
:
1.23t^2 - 2.22t + 8.5 - 90 = 0
:
1.23t^2 - 2.22t - 81.5 = 0
:
Use the quadratic formula:{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this equation: a=1.23, b=-2.22, c=-81.5
{{{t = (-(-2.22) +- sqrt(4.9284 - 4 * 1.23 * -81.5 ))/(2*1.23) }}}
:
{{{t = (2.22 +- sqrt(4.9284 - (-400.98) ))/(2.46) }}}
:
{{{t = (2.22 +- sqrt(4.9284 + 400.98 ))/(2.46) }}}
:
{{{t = (2.22 +- sqrt(405.9084 ))/(2.46) }}}
Positive solution
{{{t = (2.22 + 20.147)/2.46}}}
t = {{{22.367/2.46}}}
t = 9.09 ~ 9 yrs; 1999 is the year of 90 million dollars